This project will investigate two grand themes in macro-demographic theory: that homostatic mechanisms have led human populations to equilibrate with resources (as mediated by culture and technology), and that technological change is itself spurred by increases in population. These theories will be further developed and systematized at a formal level, with careful attention to the roles of randomness and exogenous variation, age distribution fluctuations, the integration of the two theories, and the problems of estimation and inference from both temporal and cross-sectional data. The project is interdisciplinary; while its core is economic demography, it will draw on related research in historical demography, economic history, statistics, anthropology and perhaps animal population biology. The method is to specify mathematical models embodying the theories and incorporating disturbances; to analyze the dynamic behavior of these models using phase diagrams, characteristic roots, theoretical cross-spectral variables and other procedures; and where possible to estimate the models from historical and contemporary data. These theories are central to our view of the long sweep of human history, and increasingly to our view of the human future. In them, the determinants and consequences of fertility and mortality, two health-related variables, play a central role.